Abstract :
In this paper, we present formulas for the number of decompositions of elements of the Weyl groups of type An, Dn and Bn as products of a number of reflections that is not necessarily minimal. For this purpose, we consider the poset of conjugacy classes of W introduced in for the symmetric group. This poset describes the action of the set of reflections of a reflection group on its conjugacy classes. In particular, we show how the reflection decompositions in the symmetric group %plane1D;50A;n are related to the reflection decompositions in Dn.
